2015-2016学年广东省广州市南沙区第一中学高二下学期期中考试英语试题 Word版无答案

2015-2016学年南沙一中高一第二学期中段考试题本试卷共三大题，满分为150分。

考试时间120分钟。

注意事项：1．答卷前，考生务必用黑色字迹的钢或签字笔将自己的姓名和考生号、试室号、座位号写在答题卡和答卷纸上。

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第Ⅰ卷第一部分听力（共两节，满分20分）第一节（共15小题；每小题1分，满分15分）听下面5段对话。

每段对话后有一个小题，从题中所给的A．B．C．三个选项中选出最佳选项，并标在试卷的相应位置。

听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一小题。

每段对话读两遍。

Conversation 11.What will the man do this weekend?A.Prepare for a speech.B.Visit his grandparents.C.Go to the town with John.2.Who does the man think can give a speech?A.JohnB.The woman.C.Henry.Conversation 23.What do we know about Frank?A.He doesn’t like reading.B.He learns very fast now.C.He isn’t very smart.4.What’s the most probable relationship between the two speakers?A.Teacher and student.B. Classmates.C.Colleagues.Conversation 35. What’s the date today?A.October 5th.B. October 8th.C. October 10th.6.What will the woman do tonight?A.Make a plan.B. Stay at home.C. Go to a party.Conversation 47.How does the woman usually take photos?ing a camera.ing her cellphone.ing her iPad.8.What does the woman think of cameras?A.They’re very helpful.B.They take good photos.C.They may disappear one day.9.What will the man do?A.Buy a cellphone.B.Buy a camera downtown.C.Buy a camera from eBay. Conversation 510.How does the girl look?A.UpsetB.ExcitedC.Calm.11.How much pocket money did the girl hope for a week?A.8 pounds.B.10 pounds.C.12pounds.12.Where does the boy get books from?A.Friends.B.Bookstores.C. The school library.Conversation 613.What color is the woma n’s hair?A. Golden.B.Black.C.Red.14.Where do the speakers refer to hairstyles?A.Online.B.On a phone.C.In a magazine.15.What does the woman want to do with her hair?A.Change its color.B.Cut it very short.C.Make it a bit curly.第二节（共5小题；每小题1分，满分5分）听短文填空，每个空格不得超过三个单词。

2015-2016学年广东省广州市南沙一中高二（下）期中数学试卷（理科）一、选择题（每题5分，共12题）1．（5分）因为指数函数y＝a x是增函数，是指数函数，则是增函数．这个结论是错误的，这是因为（）A．大前提错误B．小前提错误C．推理形式错误D．非以上错误2．（5分）i是虚数单位，复数等于（）A．﹣1﹣i B．1﹣i C．﹣1+i D．1+i3．（5分）曲线y＝x与y＝x3围成的封闭区域的面积是（）A．1B．C．D．4．（5分）曲线y＝x3﹣2x+4在点（1，3）处的切线的倾斜角为（）A．30°B．45°C．60°D．120°5．（5分）二项式（x﹣）9的展开式中x3的系数是（）A．84B．﹣84C．126D．﹣1266．（5分）在复平面内，复数1+i与1+3i分别对应向量，其中O为坐标原点，则＝（）A．B．2C．D．47．（5分）设f′（x）是函数f（x）的导函数，y＝f′（x）的图象如图所示，则y＝f（x）的图象最有可能是图中的（）A．B．C．D．8．（5分）某班级要从4名男生、2名女生中选派4人参加某次社区服务，如果要求至少有1名女生，那么不同的选派方案种数为（）A．14B．24C．28D．489．（5分）设（1﹣x）2015＝a0+a1x+a2x2+…+a2014x2014+a2015x2015，则a2014＝（）A．﹣2014B．2014C．﹣2015D．201510．（5分）函数y＝x3﹣2ax+a在（0，1）内有极小值，则实数a的取值范围是（）A．（0，3）B．（0，）C．（0，+∞）D．（﹣∞，3）11．（5分）在数列{a n}中，a n＝1﹣+﹣+…+﹣，则a k+1＝（）A．a k+B．a k+﹣C．a k+D．a k+﹣12．（5分）当x≥2时，lnx与的大小关系为（）A．lnx＞B．lnx＜C．lnx＝D．大小关系不确定二、填空题（每题5分，共6题）13．（5分）已知x＞0，观察下列不等式：①x，②x③x≥4，…，则第n个不等式为．14．（5分）正三棱柱体积为16，当其表面积最小时，底面边长a＝．15．（5分）设a，b∈R，a+bi＝（i为虚数单位），则a+b的值为．16．（5分）若f（x）＝﹣x2+bln（x+2）在（﹣1，+∞）上是减函数，则b的取值范围是．三、解答题17．（10分）已知复数z＝（m2﹣8m+15）+（m2﹣9m+18）i在复平面内表示的点为A，实数m取什么值时：（1）z为实数？（2）z为纯虚数？（3）A位于第三象限？18．（12分）已知数列{a n}满足a1＝2，且a n a n+1+a n+1﹣2a n＝0（n∈N+）．（1）求a2、a3、a4的值；（2）猜想数列{a n}的通项公式，并用数学归纳法加以证明．19．（12分）六人按下列要求站一横排，分别有多少种不同的站法？（1）甲不站两端；（2）甲、乙必须相邻；（3）甲、乙不相邻；（4）甲、乙按自左至右顺序排队（可以不相邻）；（5）甲、乙站在两端．20．（12分）已知二次函数f（x）＝ax2+bx﹣3在x＝1处取得极值，且在（0，﹣3）点处的切线与直线2x+y＝0平行．（1）求f（x）的解析式；（2）求函数g（x）＝xf（x）+4x的单调递增区间及极值．（3）求函数g（x）＝xf（x）+4x在x∈[0，2]的最值．21．（12分）某商品每件成本9元，售价30元，每星期卖出432件．如果降低价格．销售量可以增加，且每星期多卖出的商品件数与商品单价的降低销x （单位：元，0≤x≤30）的平方成正比．已知商品单价降低2元时，一星期多卖出24件．（Ⅰ）将一个星期的商品销售利润表示成x的函数；（Ⅱ）如何定价才能使一个星期的商品销售利润最大？22．（12分）已知函数f（x）＝e x+ax﹣1（e为自然对数的底数）．（Ⅰ）当a＝1时，求过点（1，f（1））处的切线与坐标轴围成的三角形的面积；（Ⅱ）若f（x）≥x2在（0，1）上恒成立，求实数a的取值范围．2015-2016学年广东省广州市南沙一中高二（下）期中数学试卷（理科）参考答案与试题解析一、选择题（每题5分，共12题）1．（5分）因为指数函数y＝a x是增函数，是指数函数，则是增函数．这个结论是错误的，这是因为（）A．大前提错误B．小前提错误C．推理形式错误D．非以上错误【解答】解：∵当a＞1时，函数是一个增函数，当0＜a＜1时，指数函数是一个减函数∴y＝a x是增函数这个大前提是错误的，从而导致结论错．故选：A．2．（5分）i是虚数单位，复数等于（）A．﹣1﹣i B．1﹣i C．﹣1+i D．1+i【解答】解：复数＝＝＝i﹣i2＝1+i，故选：D．3．（5分）曲线y＝x与y＝x3围成的封闭区域的面积是（）A．1B．C．D．【解答】解：如图曲线y＝x于y＝x3围成的封闭区域为图中阴影部分，其面积为2＝2（）|＝；故选：B．4．（5分）曲线y＝x3﹣2x+4在点（1，3）处的切线的倾斜角为（）A．30°B．45°C．60°D．120°【解答】解：y′＝3x2﹣2，切线的斜率k＝3×12﹣2＝1．故倾斜角为45°．故选：B．5．（5分）二项式（x﹣）9的展开式中x3的系数是（）A．84B．﹣84C．126D．﹣126【解答】解（x﹣）9的展开式的通项为T r+1＝＝，令9﹣2r＝3，解得r＝3，得到展开式中x3的项C93（﹣1）3x3＝﹣84x3，即x3的系数是﹣84，故选：B．6．（5分）在复平面内，复数1+i与1+3i分别对应向量，其中O为坐标原点，则＝（）A．B．2C．D．4【解答】解：∵复数1+i与1+3i分别对应向量，∴＝1+3i﹣1﹣i＝2i∴＝2故选：B．7．（5分）设f′（x）是函数f（x）的导函数，y＝f′（x）的图象如图所示，则y＝f（x）的图象最有可能是图中的（）A．B．C．D．【解答】解：由y＝f'（x）的图象易得当x＜0或x＞2时，f'（x）＞0，故函数y＝f（x）在区间（﹣∞，0）和（2，+∞）上单调递增；当0＜x＜2时，f'（x）＜0，故函数y＝f（x）在区间（0，2）上单调递减；故选：A．8．（5分）某班级要从4名男生、2名女生中选派4人参加某次社区服务，如果要求至少有1名女生，那么不同的选派方案种数为（）A．14B．24C．28D．48【解答】解：法一：4人中至少有1名女生包括1女3男及2女2男两种情况，故不同的选派方案种数为C12•C34+C22•C24＝2×4+1×6＝14；法二：从4男2女中选4人共有C46种选法，4名都是男生的选法有C44种，故至少有1名女生的选派方案种数为C46﹣C44＝15﹣1＝14．故选：A．9．（5分）设（1﹣x）2015＝a0+a1x+a2x2+…+a2014x2014+a2015x2015，则a2014＝（）A．﹣2014B．2014C．﹣2015D．2015【解答】解：由题意可得a2014为展开式第2015项的系数，再根据通项公式可得第2015项的系数为•（﹣1）2014＝2015，故选：D．10．（5分）函数y＝x3﹣2ax+a在（0，1）内有极小值，则实数a的取值范围是（）A．（0，3）B．（0，）C．（0，+∞）D．（﹣∞，3）【解答】解：根据题意，y'＝3x2﹣2a＝0有极小值则方程有解a＞0x＝±所以x＝是极小值点所以0＜＜10＜＜10＜a＜故选：B．11．（5分）在数列{a n}中，a n＝1﹣+﹣+…+﹣，则a k+1＝（）A．a k+B．a k+﹣C．a k+D．a k+﹣【解答】解：∵a n＝1﹣+﹣+…+﹣，∴a1＝1﹣，a2＝1﹣+﹣，…，a n＝1﹣+﹣+…+﹣，a k＝1﹣+﹣+…+﹣，所以，a k+1＝a k+﹣．故选：D．12．（5分）当x≥2时，lnx与的大小关系为（）A．lnx＞B．lnx＜C．lnx＝D．大小关系不确定【解答】解：函数y＝lnx在（0，+∞）上单调递增∴当x≥2时，lnx≥ln2＞ln1＝0而＝≤0∴lnx＞故选：A．二、填空题（每题5分，共6题）13．（5分）已知x＞0，观察下列不等式：①x，②x③x≥4，…，则第n个不等式为x．【解答】解：观察下列不等式：①x，②x③x≥4，…，可知，各个不等式左边共有两项，第一项都为x，第二项依次为，，，…，右边依次为2，3，4，…，n+1从而得满足的不等式为x．故答案为：x．14．（5分）正三棱柱体积为16，当其表面积最小时，底面边长a＝4．【解答】解：设正三棱柱的底面边长为a，高为h，则＝16，∴h＝．∴三棱柱的表面积S＝a2+＝a2++≥3＝24（a＞0）当且仅当＝即a＝4时，取等号．故答案为：4．15．（5分）设a，b∈R，a+bi＝（i为虚数单位），则a+b的值为8．【解答】解：由题，a，b∈R，a+bi＝所以a＝5，b＝3，故a+b＝8故答案为816．（5分）若f（x）＝﹣x2+bln（x+2）在（﹣1，+∞）上是减函数，则b的取值范围是b≤﹣1．【解答】解：由题意可知f′（x）＝﹣x+≤0，在x∈（﹣1，+∞）上恒成立，即b≤x（x+2）在x∈（﹣1，+∞）上恒成立，∵f（x）＝x（x+2）＝x2+2x且x∈（﹣1，+∞）∴f（x）＞﹣1∴要使b≤x（x+2），需b≤﹣1故答案为b≤﹣1．三、解答题17．（10分）已知复数z＝（m2﹣8m+15）+（m2﹣9m+18）i在复平面内表示的点为A，实数m取什么值时：（1）z为实数？（2）z为纯虚数？（3）A位于第三象限？【解答】解：（1）∵z为实数，∴m2﹣9m+18＝0，解得m＝3或6．∴当m＝3或6时，z＝0，3为实数．（2）∵z为纯虚数，∴，解得m＝5．∴当m＝5时，z＝﹣2i为纯虚数．（3）∵z在复平面内表示的点A在第三象限，∴解得3＜m＜5．∴当3＜m＜5时，A位于第三象限．18．（12分）已知数列{a n}满足a1＝2，且a n a n+1+a n+1﹣2a n＝0（n∈N+）．（1）求a2、a3、a4的值；（2）猜想数列{a n}的通项公式，并用数学归纳法加以证明．【解答】解：（1）由题得，又a1＝2，则，，…（2）猜想．证明：①当n＝1时，，故命题成立．②假设当n＝k时命题成立，即则当n＝k+1时，，故命题也成立．综上，对一切n∈N+都有成立．19．（12分）六人按下列要求站一横排，分别有多少种不同的站法？（1）甲不站两端；（2）甲、乙必须相邻；（3）甲、乙不相邻；（4）甲、乙按自左至右顺序排队（可以不相邻）；（5）甲、乙站在两端．【解答】解：（1）方法一：要使甲不站在两端，可先让甲在中间4个位置上任选1个，有A41种站法，然后其余5人在另外5个位置上作全排列有A55种站法，根据分步计数原理，共有站A41A55＝480（种）．方法二：由于甲不站两端，这两个位置只能从其余5个人中选2个人站，有A52种站法，然后中间4人有A44种站法，根据分步计数原理，共有站法A52A44＝480（种）．方法三：若对甲没有限制条件共有A66种法，甲在两端共有2A55种站法，从总数中减去这两种情况的排列数，即得所求的站法数，共有A66﹣2A55＝480（种）．（2）先把甲、乙作为一个“整体”，看作一个人，有A55种站法，再把甲、乙进行全排列，有A22种站法，根椐分步计数原理，共有A55A22＝240（种）站法．（3）因为甲、乙不相邻，中间有隔档，可用“插空法”，第一步先让甲、乙以外的4个人站队，有A44种；第二步再将甲、乙排在4人形成的5个空档（含两端）中，有A52种，故共有站法为A44A52＝480（种）．（4）先将甲、乙以外的4人从6个位置中挑选4个位置进行排列共有A64种，剩下的两个位置，左边的就是甲，右边的就是乙，全部排完，故共有A64＝360种．（5）方法一：首先考虑特殊元素，甲、乙先站两端，有A22种，再让其他4人在中间位置作全排列，有A44种，根据分步计数原理，共有A22A44＝48（种）．方法二：首先考虑两端两个特殊位置，甲、乙去站有A22种站法，然后考虑中间4个位置，由剩下的4人去站，有A44种站法，由分步计数原理共有A22A44＝48种站法．20．（12分）已知二次函数f（x）＝ax2+bx﹣3在x＝1处取得极值，且在（0，﹣3）点处的切线与直线2x+y＝0平行．（1）求f（x）的解析式；（2）求函数g（x）＝xf（x）+4x的单调递增区间及极值．（3）求函数g（x）＝xf（x）+4x在x∈[0，2]的最值．【解答】解：（1）∵f（x）＝ax2+bx﹣3，∴f′（x）＝2ax+b．∵二次函数f（x）＝ax2+bx﹣3在x＝1处取得极值，且在（0，﹣3）点处的切线与直线2x+y＝0平行，∴，解得a＝1，b＝﹣2．所以f（x）＝x2﹣2x﹣3．（2）∵f（x）＝x2﹣2x﹣3，∴g（x）＝xf（x）+4x＝x3﹣2x2+x，所以g′（x）＝3x2﹣4x+1＝（3x﹣1）（x﹣1）．令g′（x）＝0，得，x2＝1．（所以函数g（x）的单调递增区间为（﹣∞，），（1，+∞）．在x2＝1有极小值为0．在有极大值．（3）∵g（0）＝0，g（2）＝2，∴由（2）知：函数g（x）的最大值为2，最小值为0．21．（12分）某商品每件成本9元，售价30元，每星期卖出432件．如果降低价格．销售量可以增加，且每星期多卖出的商品件数与商品单价的降低销x （单位：元，0≤x≤30）的平方成正比．已知商品单价降低2元时，一星期多卖出24件．（Ⅰ）将一个星期的商品销售利润表示成x的函数；（Ⅱ）如何定价才能使一个星期的商品销售利润最大？【解答】解：（Ⅰ）设商品降价x元，则多卖的商品数为kx2，若记商品在一个星期的获利为f（x），则依题意有f（x）＝（30﹣x﹣9）（432+kx2）＝（21﹣x）（432+kx2），又由已知条件，24＝k•22，于是有k＝6，所以f（x）＝﹣6x3+126x2﹣432x+9072，x∈[0，30]．（Ⅱ）根据（Ⅰ），我们有f'（x）＝﹣18x2+252x﹣432＝﹣18（x﹣2）（x﹣12）．∴当x＝12时，f（x）达到极大值．因为f（0）＝9072，f（12）＝11664；所以定价为30﹣12＝18元能使一个星期的商品销售利润最大．22．（12分）已知函数f（x）＝e x+ax﹣1（e为自然对数的底数）．（Ⅰ）当a＝1时，求过点（1，f（1））处的切线与坐标轴围成的三角形的面积；（Ⅱ）若f（x）≥x2在（0，1）上恒成立，求实数a的取值范围．【解答】解：（I）当a＝1时，f（x）＝e x+x﹣1，f（1）＝e，f'（x）＝e x+1，f'（1）＝e+1，函数f（x）在点（1，f（1））处的切线方程为y﹣e＝（e+1）（x﹣1），即y＝（e+1）x﹣1，设切线与x轴、y轴的交点分别为A、B，∴A，B（0，﹣1），∴，∴过点（1，f（1））处的切线与坐标轴围成的三角形的面积为．（II）由f（x）≥x2得，令h（x）＝，，令k（x）＝x+1﹣e x…（6分）k'（x）＝1﹣e x，∵x∈（0，1），∴k'（x）＜0，∴k（x）在（0，1）上是减函数，∴k（x）＜k（0）＝0．因为x﹣1＜0，x2＞0，所以，∴h（x）在（0，1）上是增函数．所以h（x）＜h（1）＝2﹣e，所以a≥2﹣e…（12分）。

2015—2016学年第二学期高二期中考试英语试题第Ⅰ卷（共85分）第一部分：听力（共两节，满分20分）第一节（共5小题；每小题1分，满分5分）听下面5段对话。

每段对话后有一个小题，从题中所给的A、B、C三个选项中选出最佳选项，并标在试卷的相应位置。

听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一小题。

每段对话仅读一遍。

1. Where does this conversation probably take place?A. In a hospital.B. In a friend‟s house.C. In the man‟s house.2. What is the woman going to buy?A. A book on planes.B. Pictures of ships.C.A book on ships.3. What kind of music does the man like?A. Folk music.B. Pop music.C. Classical music.4. Why doesn‟t the woman buy the coat?A. It is expensive.B. There isn‟t her size.C. She doesn‟t like the color.5. What is the man doing?A. Finishing his homework.B. Doing physical exercise.C. Smoking on the upper floor.第二节（共15小题，每小题1分，满分15分）听下面5段对话或独白。

每段对话或独白后有几个小题，从题中所给的A、B、C三个选项中选出最佳选项，并标在试卷的相应位置。

听每段对话或独白前，你将有时间阅读各个小题，每小题5秒钟；听完后，各小题将给出5秒钟的作答时间。

每段对话或独白读两遍。

广州市南沙第一中学2015-2016第二学期中段考高二理科数学（试卷）一、选择题（每题5分，共12题）1. 有一段演绎推理是这样的：“指数函数xa y =是增函数；xy ⎪⎭⎫⎝⎛=21是指数函数；xy ⎪⎭⎫⎝⎛=21是增函数”，结论显然是错误的，原因是 A.大前提错误 B.小前提错误 C.推理形式错误 D.非以上错误 2．i 是虚数单位，复数=-31ii（ ） A ．i --1 B ．i -1 C ．i +-1 D ．i +1 3．由曲线3,y x y x ==围成的封闭图形面积为( )（A ）112(B)14(C)13(D)7124．曲线324y x x =-+在点(13)，处的切线的倾斜角为（ ） A ．30°B ．45°C ．60°D ．120°5的展开式中3x 的系数是（ ）A ．84B ．-84C ．126D ．-1266. .在复平面内, 复数1 + i 与31+i 分别对应向量和, 其中O 为坐标原点,=（ ） A.2 B.2 C. 10 D. 4 7．设()f x '是函数()f x 的导函数, ()y f x '=的图象如左图所示,则()y f x =的 图象最有可能是下图中的（ ）8．某班级要从4名男生、2名女生中选4人接受心理调查，如果要求至少有1名女生，那么不同的选法种数为（ ）A ．14B ．24C ．28D ．48 9．设201520152014201422102015)1(x a x a x a x a a x +++++=- ，则=2014a （ ） A ．﹣2014 B ．2014 C ．﹣2015 D ．201510．函数a ax x y +-=23在)1,0(内有极小值，则实数a 的取值范围为（ ）A.(0,3)B. )3,(-∞C. ),0(+∞D. )23,0(11．在数列{a n }中，a n ＝1－12＋13－14＋…＋121n -－12n，则a k ＋1等于( )A ．a k ＋121k + B ．a k ＋122k +－124k +C ．a k ＋122k + D ．a k ＋121k +－122k + 12、当2x ≥时,ln x 与212x x -的大小关系为（ ）A ．ln x ＞212x x -B ．ln x ＜212x x -C ．ln x ＝212x x - D ．大小关系不确定二、填空题（每题5分，共6题）13.已知0x >，观察下列不等式：①12x x +≥，②243x x +≥③3274x x+≥，…，则第n 个不等式为 .14．正三棱柱体积为16，当其表面积最小时，底面边长a ＝________.15．设a b ∈R ，，117ii 12ia b -+=-（i 为虚数单位），则a b +的值为 ． 16．若21()ln(2)2f x x b x =-++∞在(-1,+)上是减函数，则b 的取值范围是 __.三、解答题17.（本小题满分10分）已知复数22(815)(918)z m m m m i =-++-+在复平面内表示的点为A ，实数m 取什么值时，（1）z 为实数？z 为纯虚数？ （2）A 位于第三象限？18．（本小题满分12分）已知数列{}n a 满足21=a ，且0211=-+++n n n n a a a a （+∈N n ）。

2015－2016学年度第二学期期中考试注意事项：1.试卷笔答内容必须答在试卷边框方框线以内，否则不得分；2.试卷Ⅰ的选择题答案必须答在指定的答题卡上，否则不得分；3.试卷Ⅱ的选择题答案必须答在答题卡对应题号位置上，否则不得分。

第Ⅰ卷第一部分单项选择（共30小题，满分30分）1. _________ you like to have dinner with me this evening?A. WouldB. MustC. MayD. Can2. The letter reminds me________the good time we had spent together.A．in B．ofC．about D．on3. You must apologize ________your mother ________ your ru deness.A．to; to B．for; to C．to; for D ．for; for4. Columbus's discovery of the “New World” took place _____ ___.A. on purposeB. by accidentC. by heartD. by mistake5.--- May I ask you a question?--- Of course. _____________A．Go ahead B．Good luck C．All the best D．Cheer up6. —Would you like some more chicken?—No, thanks. I'm ________a diet and I'm trying to ________ weig ht.A．on; lose B. on; put onC. in; have D. in; lose7. Humans __________________ polluting nature.A. ought to have stoppedB. ought to be stoppingC. ought to stopD. ought have stopped8. If you cheat in the exam, you could hardly ________ it.A. throw awayB. get awayC. get away fromD. get away with9. It's wrong for us to play tricks ________our parents. A．with B．onC．to D．at10. She could not _________ for her mistake.A．account B．permit C．exist D．consult11. He _____________ the girl, trying to remember who she w as.A．stare at B．stared at C．glare at D．glance at12. He was ____________ by his grandparents and educated at a local school.A．cheer up B．dressed up C．turned up D．bro ught up13. Some films ______ education with recreation. A．combine B．pull C．admire D ．seek14. He is said to be very wealthy, but I don't understand why he is always ________.A. in debtsB. in fashionC. in memoryD. in ra gs15. I will never forget the day _________ we spent together.A. whenB. thatC. whatD. as16. ---When will the meeting ________? ---At about 11o’clock.A. break upB. break downC. break outD. brea k into17. The stamps were _________ according to their styles and f eatures.A. found outB. sorted outC. put outD. taken out18. If people continue to destroy the rainforests, many rare an imals will surely______ in the future.A. die offB. give outC. die outD. run out19. The commercial center __________ in the late 1870s.A. came fromB. came overC. came into beingD. c ame out20. ---Would you permit me _________ here?---Sorry. We don’t permit ________ here in the reading room. A. smoking; smoking B. to smoke; to smokeC. smoking; to smokeD. to smoke; smoking21. He __________ the big tree to make some tables.A. cut outB. cut upC. cut offD. cut down22.--- Must I finish the work today?--- No, you ____________.A. needn’tB. mustn’tC. can’tD. oughtn’t to23. It was _________ that Gina was lying.A. religiousB. rawC. obviousD. indeedputers ___________ in offices and homes since 1970s.A. have been usedB. have usedC. were being usedD. used25. ---His girl friend deserted him because of his taking drugs. --He is doing what he could to _________ her love.A. win overB. win backC. win throughD. win out26. It’s possible to hold one’s _______ for three minutes, with practice.A. breathsB. breathC. breatheD. breathed27. They were searching for a way to ________ people in public life from gunfire.A. protectB. seekC. huntD. gather28. We are looking forward to __________ from you soon.A. hearB. heardC. hearingD. be heard29. The train ___________ he is travelling is arriving.A. by whichB. whatC. whichD. that30. I congratulate my neighbor, _________ son has just won the election.A. whoB. whomC. whoseD. that第二部分阅读理解（共两节，满分40分）第一节（共15小题；每小题2分，满分30分）阅读下列短文，从每题所给的四个选项（A、B、C和D）中，选出最佳选项并在答题卡上将该项涂黑。

广东省广州市南沙区2016-2017学年高二英语下学期期中试题第一部分阅读理解（共两节，满分40分）第一节（共15小题，每小题2分，共30分）阅读下列短文，从每题所给的四个选项（A、B、C和D）中，选出最佳选项。

AFor the first time in Hong Kong’s history, an entertainer has been written into middle school textbooks. He is considered one of the best actors in Hong Kong. Yes, he is Chow Yun-fat.The example of his long hard struggle for success has been used in a chapter in a Hong Kong middle school textbook. Using his experience, students can learn to make the most of their time and grab every opportunity to succeed.On hearing about this, Chow said happily, “I really hope that my experiences can make young people understand that one should not be afraid of difficulties and setbacks, for they are the only way to success.”Indeed, Chow has traveled a long and difficult path to reach his success. In 1955, he was born into a poor family in Hong Kong. When he was 17, he had to leave school. He worked in a number of jobs---- as a postman, camera salesman and taxi driver. These experiences paved the way for him to play all kinds of roles later in life.Chow broke into the film industry in the late 1970s. He was one of the hardest working actors and starred in a number of popular TV dramas and films including” Shanghai Bund”and “ A Better Tomorrow”. Since 1985, he has won many awards including Taiwan’s Golden Horse Awards and Hong Kong Film Awards.In 1995, he went to Hollywood. Although he was already in his 40s, he had to learn English. He even put chopsticks in his mouth to practice pronouncing certain sounds.His film, “Crouching Tiger, Hid den Dragon”, began to gain him more fame and recognition around the world. In 1998, the mayor of Chicago set aside January 12 as Chow Yun-fat Day.”1. Chow Yun-fat has been written into middle school textbooks mainly because ___.A. he plays best in Hong KongB. his experi ences are very specialC he keeps on struggling for successD. he is well thought of2. Chow Yun-fat felt ___ when he learned that he had been written into middle school text books.A. surprisedB. sadC. shyD. happy3. What can we infer from the passage?A. Chow Yun-fat is proud of his success.B. Chow Yun-fat is popular both at home and abroad.C. Chow Yun-fat prefers to make a living by selling cameras rather than by perform ing.D. Chow Yun-fat has won more awards than other actors.4. The underlined sentence suggests ___.A. chopsticks if of great help to practice English pronunciationB. Chow Yun-fat is willing to struggle with difficultiesC. Chow Yun-fat has suffered a lot since he went to HollywoodD. it is hard for a person who is over 40 years old to learn spoken English5. The author wrote this passage to ___.A. introduce Chow’s way to successB. praise Chow for his excellent performanceC. call on people to learn from ChowD. show why Chow is popularBHappy birthday! Do birthdays really make people happy? Of course they do. Birthdays celebrate the day we were born. Besides, that extra candle on the cake suggests anotheryear of growth and maturity（成熟）---or so we hope. We all like to imagine that we’re getting wiser and not just older. Most of us enjoy seeing the miracle of growth in others,as well. For instance, seeing our children develop and learn new things makes us feel proud.For Americans, like people in most cultures, growing up is a wonderful process. But growing old? That’s a different story.Growing old is not exactly pleasant for people in youth-oriented American culture. Most Americans like to look young, act young and feel young. As the old saying goes, “You’reas young as you feel.”Older people joke about how many years young they are, rather than how many years old. People in some countries value the aged as a source of experience and wisdom. But Americans seem to favor those that are young, or at least “young at heart”.Many older Americans find the “golden years” to be anything but golden. Economically, “senior citizens” often struggle just to get by. Retirement at age 65 brings a sharp decrease in personal income. Social security benefits usually cannot make up the difference. Older people may suffer from poor nutrition, medical care and housing. Some even experience age discrimination（歧视）. In 1987, American sociologist Pat Moore dressed up like an older person and wandered city streets. She was often treated rudely---even cheated and robbed. However, dressed as a young person, she received much more respect.Unfortunately, the elderly population in America is increasing fast. Why? People are living together. Fewer babies are being born. And middle-aged “baby borners”are rapidly entering the groups of the elderly. America may soon be a place where wrinkles（皱纹）are “in”. Marketing experts are already noticing this group of consumers.6. We can infer from the second paragraph that .A. young people lack experience and wisdomB. American older people often joke about their old ageC. American culture is very youngD. different countries have different opinions on the old age7. The main idea of the third paragraph is .A. the golden years can make the old earn lots of money and receive good medical careB. the old people in America are leading a hard life without good nutrition, medicalcare or housingC. the old in America have to retire at the age of 65D. American social security benefits are not good8.From the last paragraph we know that the underlined word “in”can be replaced by________ .A. seriousB. badC. disappearing slowlyD. growing fast9. What should be mentioned in the following paragraph?A. The public will change their attitude towards old people.B. People will provide more services to the old in their communitiesC. The government will pass laws to ensure the benefits of the oldD. Companies will soon produce more goods for old Americans10. From this passage we can know .A. in America, growing up is as wonderful a process as growing oldB. in America, growing up is a wonderful process, while growing old is notC. in America, growing old is a wonderful process, while growing up is notD. in America, growing up is not a wonderful processCHarvard researchers have created a tough, low-cost, biodegradable (可生物降解的) material inspired by insects" hard outer shells. The material"s inventors say it has a number of possible uses and someday could provide a more environmentally friendly alternative to plastic. The material, made from shrimp ("虾) shells and proteins produced from silk, is called "shrilk." It is thin, clear, flexible and strong.A major benefit of the material is its biodegradability. Plastic"s toughness and flexibility represented a revolution in materials science during the 1950s and "60s. Decades later, however, plastic"s very durability (耐用性) is raising questions about how appropriate it is for one-time products such as plastic bags, or short-lived consumer goods, used in the home for a few years and then cast into a landfill where they will degrade for centuries. What is the point of making something that lasts 1,000 years?Shrilk not only will degrade in a landfill, but its basic components are used as fertilizer (肥料), and so will enrich the soil.Shrilk has great potential, the inventors said. Materials from which it is made are plentiful in nature, found in everything ranging from shrimp shells, insect bodies to living plants. That makes shrilk low cost, and its mass production possible should it be used for products demanding a lot of material.Work on shrilk is continuing in the lab. The inventors said the material becomes flexible when wet, so they"re exploring ways to use it in wet environments. They"re also developing simpler production processes, which could be used for non-medical products, like forcomputer cases and other products inside the home. They"re even exploring combining it with other materials, like carbon fibers, to give it new properties.11: Paragraph I of the passage is mainly about shritk"s_____.A．remarkable design B．interesting nameC．major characteristics D．basic elements12: What has become a concern about plastic?A．Using it properly. B．Producing it cheaply.C．Developing its properties quickly. D．Evaluating its contributions fairly. 13: According to the inventors, shrilk has great potential partly because_____.A．it can help plastic degrade B．it can be found in living thingsC．its mass production has been realized D．its raw materials are abundant in nature 14:What are t he inventors doing in the lab?A．Replacing carbon fibers with shrilk.B．Testing ahrilk"s use in wet conditions.C．Making shrilk out of used household goods.D．Improving shrilk"s flexibility for medical purposes.15:Which of the following can be the best title for the pa ssage?A．Recent Progress in Environmental ProtectionB．Benefits of Insects in Scientific ResearchC．The Harm of One-time ProductsD．A Possible Alternative to PlasticD第二节（共5小题，每小题2分，满分10分）根据短文内容，从短文后的选项中选出能填入空白处的最佳选项。

2015-2016学年第二学期期末教学质量检测高一英语(本试卷135分，共8页)注意事项：1. 本试卷分第I卷（选择题）和第II卷（非选择题）两部分。

2. 全部答案在答题卡上完成，答在本试卷上无效。

3. 考试结束后，将答题卡交回。

第I卷第一部分阅读（共两节；满分40分）第一节（共15小题；每小题2分，满分30分）阅读下列短文，从每小题所给的四个选项（A、B、C和D）中，选出最佳选项，并在答题卡上将该项涂黑。

AMost people agree that eating healthy food is important. But sometimes making good food choices can be difficult. Now, there are apps that can help people learn about the food they eat to improve their health and their dining out experience.OpenTable appOpenTable app helps people choose restaurants when they want to go out to eat. It is a free service that shows users restaurant available based on where and when they want to dine. It gives users points when they make reservations(保留，预定), which can add up to discounts on restaurant visits.Max McCalman’s Cheese & Wine Pairing appWine and cheese can be a great combination. But which wines go best with which cheeses? Max McCalman’s Cheese & Wine Pairing app can help. It provides inf ormation about hundreds of different cheeses and suggests wines to pair with each. Max McCalman’s Cheese & Wine Pairing app is free.HappyCow appVegetarians do not eat animal meat. Vegans do not eat any animal products. The HappyCow app is made for both groups. Users can search for vegetarian-vegan restaurants and stores around the world.LocalEats appRestaurant chains, like McDonalds, can be found almost anywhere a person might travel. But sometimes travelers want to eat like locals. The LocalEats app is designed for that. It can help you find local restaurants in major cities in the US and in other countries. It costs about a dollar. Where Chefs Eat app“Where Chefs Eat” is a 975-page book. Most people would not want to carry that around. But there is a much lighter app version of the same name for just $15. Six hundred chefs provide information on 3,000 restaurants around the world on the Where Chefs Eat app.1. Happycow app is designed for those who prefer .A. local foodsB. wine and cheeseC. vegetablesD. animal meat2. What app costs you most according to the text?A. OpenTable.B. Where Chefs EatC. LocalEatsD. Max Mc Calman’s Cheese & Wine Pairing.3. Where does this passage most probably come from?A. A science textbook.B. A tourist map.C. A museum guide.D. A technology report.BIt is difficult for doctors to help a person with a damaged brain. Without enough blood, the brain lives for only three to five minutes. More often the doctors can’t fix the damage. Sometimes, they are afraid to try something to help because it is dangerous to work on the brain. The doctors might make the person worse if he operates on the brain.Dr. Robert White, a famous professor and doctor, thinks he knows a way to help. He thinks doctors should make the brain very cold. If it is very cold, the brain can live without blood for 30 minutes. This gives the doctor a longer time to do something for the brain.Dr. White tried his idea on 13 monkeys. First he taught them to do different jobs, then he operated on them. He made the monkeys’ blood go through a machine. The machine cooled the blood. Then the machine sent the blood back to the monkeys’ brains. When the brain’s temperature was 10℃, Dr. White stopped the blood to the brain. After 30 minutes he turned the blood back on. He warmed the blood again. After their operations the monkeys were like what they had been before. They were healthy and busy. Each one could still do the jobs the doctor had taught them.4. The biggest difficulty in operating on the damaged brain is that .A. the time is too short for doctorsB. the patients are often too nervousC. the damage is extremely hard to fixD. the blood-cooling machine might break down5. With Dr. White’s new idea, the oper ation on the damaged brain .A. can last as long as 30 minutesB. can keep the brain’s blood warmC. can keep the patient’s brain healthyD. can help monkeys do different jobs6. What is the right order of the steps in the operation?a. send the cooled blood back to the brainb. stop the blood to the brainc. have the blood cooled downd. operate on the brainA. a, b, c, dB. c, a, b, dC. c, b, d, aD. b, c, d, a7. What mainly makes the brain operation possible?A. Taking the blood out of the brain.B. Trying the operation on monkeys first.C. Having the blood go through a machine.D. L owering the brain’s temperature.CIf we want to deal with the association(社交) between boys and girls properly, here are some “dos and don’ts” for you to follow.Keep a normal and healthy state of mind. Our schools and classes are made up of boys and girls. It is very nature for the boys and girls to make friends with each other. We should make as many friends as possible. We should keep in touch with the other sex in public instead of in secret.Don’t be too nervous or too shy. If you are a shy person, you can also find a way out. You can make friends with the students who have the same interest and hobby as you. As both of youhave much in common, you may have much to talk about. If you keep doing like that, little by little, you will gladly find you are also as free to express yourself as others.Don’t fall into the ditch of early love. The boys and girls at a adolescence (青春期) are rich in feeling. They are easy to regard the friendship as a sign of love and fall in love with each other at an early age. In my opinion, early love is a green apple that can’t be eaten. An apple won’t taste sweet until it is full ripe. Boys and girls at middle school are too young to carry the heavy duty of love. Do keep out of early love.8. We should keep in touch with the other sex in following ways EXCEPT .A. with a good state of mindB. in real friendshipC. in publicD. in secret9. If you are a shy person, you can .A. find friends with the same interest and hobbyB. only have a few friends of the same sexC. not make friends with the other sexD. not fall in love with other students easily10. What does the underlined sentence probably mean?A. Don’t get into the habit of early love.B. Don’t be addicted to early love.C. Don’t be trapped in early love.D. Don’t be confused by early love.11. The main idea of the passage is to .A. tell students to keep away from early loveB. give some advice on how to associate between boys and girlsC. tell students how to make friendsD. teach boys how to talk with girlsDTwelve years ago, I arrived in Central Florida from Puerto Rico. I had heard of a job opportunity and decided to pursue it, but it never became a reality. I quickly learned that being alone without resources in an unfamiliar city was not a comfortable situation to be in.Once my limited funds ran out I became homeless and spent a year and a half living on the streets of Orlando. Apart from feeling not being noticed and missing my family, I had to face another challenge—hunger.For the first time in my life, I, as a foreign man, who had lived my life in the relative comfort of the middle class, understood the frustration someone feels when they don’t get enough to eat.I clearly remembered having run a distance of more than 7 miles on many occasions just to make it to a local feeding program before they closed at 7 pm.Once the need for food was met, the next challenge would arise—where to find a place to sleep for the night. Fortunately, local programs like the Coalition for the Homeless, Second Harvest Food Bank and the Wayne Densch Center were an important part of my ability to survive my painful experience.With the help of these programs, I was accepted by a college scholarship program through the Coalition and obtained two degrees from Valencia.My experience has helped me understand that devoting my life to helping others offers lasting rewards. Today, I am employed as Childhood Hunger Programs Manager at Second Harvest Food Bank and oversee the summer feeding, Hi-Five Kids Pack, and Kids Café programs. Iam so proud to be able to distribute food resources to those wonderful programs and help hundreds more like me.12. What can be inferred from Paragraph 1?A. The author wouldn’t go to Central Florida again.B. The author felt hopeless in Central Florida at that time.C. Florida was not a good place for people living there at that time.D. People like to live with friends in a familiar city.13. Why did the author run a distance of over 7 miles on many occasions?A. Because he didn’t want to be late for work there.B. Because he desired to get some food to eat.C. Because he went there to help the poor.D. Because he helped distribute food resources to the poor.14. Before being accepted by a college scholarship program, the author .A. had lived with his relatives happilyB. had won his degree in a universityC. had been struggling financiallyD. had lost hope of facing the future15. From his experience, the author learns that .A. people can learn a lesson from difficultiesB. people may suffer a lot in an unfamiliar cityC. people should not give up even in troubleD. people might be rewarded if they’re kind to others第二节（共5小题；每小题2分，满分10分）根据短文内容，从短文后的（A、B、C、D、E、F、G）选项中选出能填入空白处的最佳选项，选项中有两项为多余选项。

2015-2016学年广东省广州市南沙一中高二（下）期中数学试卷（理科）一、选择题（每题5分，共12题）1．因为指数函数y=a x是增函数，是指数函数，则是增函数．这个结论是错误的，这是因为（）A．大前提错误B．小前提错误C．推理形式错误 D．非以上错误2．i是虚数单位，复数等于（）A．﹣1﹣i B．1﹣i C．﹣1+i D．1+i3．曲线y=x与y=x3围成的封闭区域的面积是（）A．1 B．C．D．4．曲线y=x3﹣2x+4在点（1，3）处的切线的倾斜角为（）A．30°B．45°C．60°D．120°5．二项式（x﹣）9的展开式中x3的系数是（）A．84 B．﹣84 C．126 D．﹣1266．在复平面内，复数1+i与1+3i分别对应向量，其中O为坐标原点，则=（）A．B．2 C． D．47．设f′（x）是函数f（x）的导函数，y=f′（x）的图象如图所示，则y=f（x）的图象最有可能是图中的（）A．B．C．D．8．某班级要从4名男生、2名女生中选派4人参加某次社区服务，如果要求至少有1名女生，那么不同的选派方案种数为（）A．14 B．24 C．28 D．489．设（1﹣x）2015=a0+a1x+a2x2+…+a2014x2014+a2015x2015，则a2014=（）A．﹣2014 B．2014 C．﹣2015 D．201510．函数y=x3﹣2ax+a在（0，1）内有极小值，则实数a的取值范围是（）A．（0，3）B．（0，）C．（0，+∞）D．（﹣∞，3）11．在数列{a n}中，a n=1﹣+﹣+…+﹣，则a k+1=（）A．a k+ B．a k+﹣C．a k+ D．a k+﹣12．当x≥2时，lnx与的大小关系为（）A．lnx＞B．lnx＜C．lnx= D．大小关系不确定二、填空题（每题5分，共6题）13．已知x＞0，观察下列不等式：①x，②x③x≥4，…，则第n个不等式为．14．正三棱柱体积为16，当其表面积最小时，底面边长a=．15．设a，b∈R，a+bi=（i为虚数单位），则a+b的值为．16．若f（x）=﹣x2+bln（x+2）在（﹣1，+∞）上是减函数，则b的取值范围是．三、解答题17．已知复数z=（m2﹣8m+15）+（m2﹣9m+18）i在复平面内表示的点为A，实数m取什么值时：（1）z为实数？（2）z为纯虚数？（3）A位于第三象限？18．已知数列{a n}满足a1=2，且a n a n+1+a n+1﹣2a n=0（n∈N+）．（1）求a2、a3、a4的值；（2）猜想数列{a n}的通项公式，并用数学归纳法加以证明．19．六人按下列要求站一横排，分别有多少种不同的站法？（1）甲不站两端；（2）甲、乙必须相邻；（3）甲、乙不相邻；（4）甲、乙按自左至右顺序排队（可以不相邻）；（5）甲、乙站在两端．20．已知二次函数f（x）=ax2+bx﹣3在x=1处取得极值，且在（0，﹣3）点处的切线与直线2x+y=0平行．（1）求f（x）的解析式；（2）求函数g（x）=xf（x）+4x的单调递增区间及极值．（3）求函数g（x）=xf（x）+4x在x∈[0，2]的最值．21．某商品每件成本9元，售价30元，每星期卖出432件．如果降低价格．销售量可以增加，且每星期多卖出的商品件数与商品单价的降低销x（单位：元，0≤x≤30）的平方成正比．已知商品单价降低2元时，一星期多卖出24件．（Ⅰ）将一个星期的商品销售利润表示成x的函数；（Ⅱ）如何定价才能使一个星期的商品销售利润最大？22．已知函数f（x）=e x+ax﹣1（e为自然对数的底数）．（Ⅰ）当a=1时，求过点（1，f（1））处的切线与坐标轴围成的三角形的面积；（Ⅱ）若f（x）≥x2在（0，1）上恒成立，求实数a的取值范围．2015-2016学年广东省广州市南沙一中高二（下）期中数学试卷（理科）参考答案与试题解析一、选择题（每题5分，共12题）1．因为指数函数y=a x是增函数，是指数函数，则是增函数．这个结论是错误的，这是因为（）A．大前提错误B．小前提错误C．推理形式错误 D．非以上错误【考点】演绎推理的基本方法．【分析】对于指数函数来说，底数的范围不同，则函数的增减性不同，当a＞1时，函数是一个增函数，当0＜a＜1时，指数函数是一个减函数y=a x是增函数这个大前提是错误的，得到结论【解答】解：∵当a＞1时，函数是一个增函数，当0＜a＜1时，指数函数是一个减函数∴y=a x是增函数这个大前提是错误的，从而导致结论错．故选A．2．i是虚数单位，复数等于（）A．﹣1﹣i B．1﹣i C．﹣1+i D．1+i【考点】复数代数形式的乘除运算．【分析】根据两个复数代数形式的乘除法法则，以及虚数单位i的幂运算性质，把要求的式子化简求得结果．【解答】解：复数===i﹣i2=1+i，故选D．3．曲线y=x与y=x3围成的封闭区域的面积是（）A．1 B．C．D．【考点】定积分在求面积中的应用．【分析】画出图形，利用定积分的几何意义，将面积表示为定积分的形式，计算定积分即可．【解答】解：如图曲线y=x于y=x3围成的封闭区域为图中阴影部分，其面积为2=2（）|=；故选B．4．曲线y=x3﹣2x+4在点（1，3）处的切线的倾斜角为（）A．30°B．45°C．60°D．120°【考点】导数的几何意义．【分析】欲求在点（1，3）处的切线倾斜角，先根据导数的几何意义可知k=y′|x=1，再结合正切函数的值求出角α的值即可．【解答】解：y/=3x2﹣2，切线的斜率k=3×12﹣2=1．故倾斜角为45°．故选B．5．二项式（x﹣）9的展开式中x3的系数是（）A．84 B．﹣84 C．126 D．﹣126【考点】二项式定理的应用．【分析】由题意知利用二项展开式的通项公式写出展开式的通项，令x的指数为3，写出出展开式中x3的系数，得到结果．【解答】解（x﹣）9的展开式的通项为T r+1==，令9﹣2r=3，解得r=3，得到展开式中x3的项C93（﹣1）3x3=﹣84x3，即x3的系数是﹣84，故选：B6．在复平面内，复数1+i与1+3i分别对应向量，其中O为坐标原点，则=（）A．B．2 C． D．4【考点】复数求模；复数的基本概念．【分析】根据所给的两个向量的代数形式，先求两个向量的差，求出，得到向量的代数形式的表示式，根据模长公式做出要求向量的模长．【解答】解：∵复数1+i与1+3i分别对应向量，∴=1+3i﹣1﹣i=2i∴=2故选B．7．设f′（x）是函数f（x）的导函数，y=f′（x）的图象如图所示，则y=f（x）的图象最有可能是图中的（）A．B．C．D．【考点】利用导数研究函数的单调性．【分析】先根据导函数的图象确定导函数大于0 的范围和小于0的x的范围，进而根据当导函数大于0时原函数单调递增，当导函数小于0时原函数单调递减确定原函数的单调增减区间．【解答】解：由y=f'（x）的图象易得当x＜0或x＞2时，f'（x）＞0，故函数y=f（x）在区间（﹣∞，0）和（2，+∞）上单调递增；当0＜x＜2时，f'（x）＜0，故函数y=f（x）在区间（0，2）上单调递减；故选A8．某班级要从4名男生、2名女生中选派4人参加某次社区服务，如果要求至少有1名女生，那么不同的选派方案种数为（）A．14 B．24 C．28 D．48【考点】排列、组合的实际应用．【分析】法一：用直接法，4人中至少有1名女生包括1女3男及2女2男两种情况，计算各种情况下的选派方案种数，由加法原理，计算可得答案；法二：用排除法，首先计算从4男2女中选4人的选派方案种数，再计算4名都是男生的选派方案种数，由排除法，计算可得答案．【解答】解：法一：4人中至少有1名女生包括1女3男及2女2男两种情况，故不同的选派方案种数为C12•C34+C22•C24=2×4+1×6=14；法二：从4男2女中选4人共有C46种选法，4名都是男生的选法有C44种，故至少有1名女生的选派方案种数为C46﹣C44=15﹣1=14．故选A．9．设（1﹣x）2015=a0+a1x+a2x2+…+a2014x2014+a2015x2015，则a2014=（）A．﹣2014 B．2014 C．﹣2015 D．2015【考点】二项式系数的性质．【分析】由题意可得a2014展开式第2015项的系数，再根据通项公式可得第2015项的系数．【解答】解：由题意可得a2014为展开式第2015项的系数，再根据通项公式可得第2015项的系数为•（﹣1）2014=2015，故选：D．10．函数y=x3﹣2ax+a在（0，1）内有极小值，则实数a的取值范围是（）A．（0，3）B．（0，）C．（0，+∞）D．（﹣∞，3）【考点】函数在某点取得极值的条件．【分析】先对函数求导，函数在（0，1）内有极小值，得到导函数等于0时，求出x的值，这个值就是函数的极小值点，使得这个点在（0，1）上，求出a的值．【解答】解：根据题意，y'=3x2﹣2a=0有极小值则方程有解a＞0x=±所以x=是极小值点所以0＜＜10＜＜10＜a＜故选B11．在数列{a n}中，a n=1﹣+﹣+…+﹣，则a k+1=（）A．a k+ B．a k+﹣C．a k+ D．a k+﹣【考点】数列的概念及简单表示法．【分析】由已知中a n=1﹣+﹣+…+﹣，我们依次给出a1，a2，…，a n，a k的表达式，分析变化规律，即可得到a k+1的表达式．【解答】解：∵a n=1﹣+﹣+…+﹣，∴a1=1﹣，a2=1﹣+﹣，…，a n=1﹣+﹣+…+﹣，a k=1﹣+﹣+…+﹣，所以，a k+1=a k+﹣．故选：D．12．当x≥2时，lnx与的大小关系为（）A．lnx＞B．lnx＜C．lnx= D．大小关系不确定【考点】不等式比较大小．【分析】本题lnx（x≥2）时为正数，只要将变形判断正负即可．【解答】解：函数y=lnx在（0，+∞）上单调递增∴当x≥2时，lnx≥ln2＞ln1=0而=≤0∴lnx＞故选A二、填空题（每题5分，共6题）13．已知x＞0，观察下列不等式：①x，②x③x≥4，…，则第n个不等式为x．【考点】归纳推理．【分析】根据不等式：①x，②x③x≥4，…，结合左右两边式子的特点，可以猜测第n个不等式x．【解答】解：观察下列不等式：①x，②x③x≥4，…，可知，各个不等式左边共有两项，第一项都为x，第二项依次为，，，…，右边依次为2，3，4，…，n+1从而得满足的不等式为x．故答案为：x．14．正三棱柱体积为16，当其表面积最小时，底面边长a=4．【考点】棱柱、棱锥、棱台的体积．【分析】设底面边长为a，根据体积公式用a表示出高h，得出表面积S关于a的函数，利用基本不等式得出答案．【解答】解：设正三棱柱的底面边长为a，高为h，则=16，∴h=．∴三棱柱的表面积S=a2+=a2++≥3=24（a＞0）当且仅当=即a=4时，取等号．故答案为：4．15．设a，b∈R，a+bi=（i为虚数单位），则a+b的值为8．【考点】复数代数形式的乘除运算；复数相等的充要条件．【分析】由题意，可对复数代数式分子与分母都乘以1+2i，再由进行计算即可得到a+bi=5+3i，再由复数相等的充分条件即可得到a，b的值，从而得到所求的答案【解答】解：由题，a，b∈R，a+bi=所以a=5，b=3，故a+b=8故答案为816．若f（x）=﹣x2+bln（x+2）在（﹣1，+∞）上是减函数，则b的取值范围是b≤﹣1．【考点】函数单调性的性质；利用导数研究函数的单调性．【分析】根据函数在（﹣1，+∞）上是减函数，对函数f（x）进行求导，判断出f′（x）＜0进而根据导函数的解析式求得b的范围．【解答】解：由题意可知f′（x）=﹣x+≤0，在x∈（﹣1，+∞）上恒成立，即b≤x（x+2）在x∈（﹣1，+∞）上恒成立，∵f（x）=x（x+2）=x2+2x且x∈（﹣1，+∞）∴f（x）＞﹣1∴要使b≤x（x+2），需b≤﹣1故答案为b≤﹣1．三、解答题17．已知复数z=（m2﹣8m+15）+（m2﹣9m+18）i在复平面内表示的点为A，实数m取什么值时：（1）z为实数？（2）z为纯虚数？（3）A位于第三象限？【考点】复数的代数表示法及其几何意义．【分析】利用复数的几何意义、及复数为实数、纯虚数的充要条件即可得出．【解答】解：（1）∵z为实数，∴m2﹣9m+18=0，解得m=3或6．∴当m=3或6时，z=0，3为实数．（2）∵z为纯虚数，∴，解得m=5．∴当m=5时，z=﹣2i为纯虚数．（3）∵z在复平面内表示的点A在第三象限，∴解得3＜m＜5．∴当3＜m＜5时，A位于第三象限．18．已知数列{a n}满足a1=2，且a n a n+1+a n+1﹣2a n=0（n∈N+）．（1）求a2、a3、a4的值；（2）猜想数列{a n}的通项公式，并用数学归纳法加以证明．【考点】数学归纳法；数列递推式．【分析】（1）由题意可得，又a1=2，可求得a2，再由a2的值求a3，再由a3的值求出a4的值．（2）猜想，检验n=1时等式成立，假设n=k时命题成立，证明当n=k+1时命题也成立．【解答】解：（1）由题得，又a1=2，则，，…（2）猜想．证明：①当n=1时，，故命题成立．②假设当n=k时命题成立，即则当n=k+1时，，故命题也成立．综上，对一切n∈N+都有成立．19．六人按下列要求站一横排，分别有多少种不同的站法？（1）甲不站两端；（2）甲、乙必须相邻；（3）甲、乙不相邻；（4）甲、乙按自左至右顺序排队（可以不相邻）；（5）甲、乙站在两端．【考点】排列、组合及简单计数问题．【分析】（1）根据题意，首先分析甲的情况，易得甲有4种情况，再将剩余的5个人进行全排列，安排在其余5个位置，由分步计数原理计算可得答案；（2）根据题意，先把甲、乙作为一个“整体”，看作一个人，再把甲、乙进行全排列，由分步计数原理计算可得答案；（3）根据题意，因为甲、乙不相邻，中间有隔档，可用“插空法”，第一步先让甲、乙以外的4个人站队；第二步再将甲、乙排在4人形成的5个空档（含两端）中，由分步计数原理计算可得答案；（4）根据题意，先将甲、乙以外的4人从6个位置中挑选4个位置进行排列共有A64种，剩下的两个位置，左边的就是甲，右边的就是乙，问题得以解决．（5）根据题意，首先考虑特殊元素，甲、乙先站两端，再让其他4人在中间位置作全排列，根据分步计数原理，由分步计数原理计算可得答案【解答】解：（1）方法一：要使甲不站在两端，可先让甲在中间4个位置上任选1个，有A41种站法，然后其余5人在另外5个位置上作全排列有A55种站法，根据分步计数原理，共有站A41A55=480（种）．方法二：由于甲不站两端，这两个位置只能从其余5个人中选2个人站，有A52种站法，然后中间4人有A44种站法，根据分步计数原理，共有站法A52A44=480（种）．方法三：若对甲没有限制条件共有A66种法，甲在两端共有2A55种站法，从总数中减去这两种情况的排列数，即得所求的站法数，共有A66﹣2A55=480（种）．（2）先把甲、乙作为一个“整体”，看作一个人，有A55种站法，再把甲、乙进行全排列，有A22种站法，根椐分步计数原理，共有A55A22=240（种）站法．（3）因为甲、乙不相邻，中间有隔档，可用“插空法”，第一步先让甲、乙以外的4个人站队，有A44种；第二步再将甲、乙排在4人形成的5个空档（含两端）中，有A52种，故共有站法为A44A52=480（种）．（4）先将甲、乙以外的4人从6个位置中挑选4个位置进行排列共有A64种，剩下的两个位置，左边的就是甲，右边的就是乙，全部排完，故共有A64=360种．（5）方法一：首先考虑特殊元素，甲、乙先站两端，有A22种，再让其他4人在中间位置作全排列，有A44种，根据分步计数原理，共有A22A44=48（种）．方法二：首先考虑两端两个特殊位置，甲、乙去站有A22种站法，然后考虑中间4个位置，由剩下的4人去站，有A44种站法，由分步计数原理共有A22A44=48种站法．20．已知二次函数f（x）=ax2+bx﹣3在x=1处取得极值，且在（0，﹣3）点处的切线与直线2x+y=0平行．（1）求f（x）的解析式；（2）求函数g（x）=xf（x）+4x的单调递增区间及极值．（3）求函数g（x）=xf（x）+4x在x∈[0，2]的最值．【考点】利用导数求闭区间上函数的最值；利用导数研究函数的单调性；利用导数研究函数的极值．【分析】（1）由f（x）=ax2+bx﹣3，知f′（x）=2ax+b．由二次函数f（x）=ax2+bx﹣3在x=1处取得极值，且在（0，﹣3）点处的切线与直线2x+y=0平行，知，由此能求出f（x）．（2）由f（x）=x2﹣2x﹣3，知g（x）=xf（x）+4x=x3﹣2x2+x，所以g′（x）=3x2﹣4x+1=（3x﹣1）（x﹣1）．令g′（x）=0，得，x2=1．列表讨论能求出函数g（x）=xf（x）+4x的单调递增区间及极值．（3）由g（0）=0，g（2）=2，结合（2）的结论，能求出函数g（x）的最大值和最小值．【解答】解：（1）∵f（x）=ax2+bx﹣3，∴f′（x）=2ax+b．∵二次函数f（x）=ax2+bx﹣3在x=1处取得极值，且在（0，﹣3）点处的切线与直线2x+y=0平行，∴，解得a=1，b=﹣2．所以f（x）=x2﹣2x﹣3．（2）∵f（x）=x2﹣2x﹣3，∴g（x）=xf（x）+4x=x3﹣2x2+x，所以g′（x）=3x2﹣4x+1=（3x﹣1）（x﹣1）．令g′（x）=0，得，x2=1．极大值所以函数g（x）的单调递增区间为（﹣∞，），（1，+∞）．在x2=1有极小值为0．在有极大值．（3）∵g（0）=0，g（2）=2，∴由（2）知：函数g（x）的最大值为2，最小值为0．21．某商品每件成本9元，售价30元，每星期卖出432件．如果降低价格．销售量可以增加，且每星期多卖出的商品件数与商品单价的降低销x（单位：元，0≤x≤30）的平方成正比．已知商品单价降低2元时，一星期多卖出24件．（Ⅰ）将一个星期的商品销售利润表示成x的函数；（Ⅱ）如何定价才能使一个星期的商品销售利润最大？【考点】函数模型的选择与应用．【分析】（Ⅰ）先设商品降价x元，写出多卖的商品数，则可计算出商品在一个星期的获利数，再依题意：“商品单价降低2元时，一星期多卖出24件”求出比例系数即可得一个星期的商品销售利润表示成x的函数；（Ⅱ）根据（Ⅰ）中得到的函数，利用导数研究其极值，从而救是f（x）达到极大值．从而得出所以定价为多少元时，能使一个星期的商品销售利润最大．【解答】解：（Ⅰ）设商品降价x元，则多卖的商品数为kx2，若记商品在一个星期的获利为f（x），则依题意有f（x）=（30﹣x﹣9）=（21﹣x），又由已知条件，24=k•22，于是有k=6，所以f（x）=﹣6x3+126x2﹣432x+9072，x∈[0，30]．2（x﹣2）（x﹣12）．∴当时，（）达到极大值．因为f（0）=9072，f（12）=11664；所以定价为30﹣12=18元能使一个星期的商品销售利润最大．22．已知函数f（x）=e x+ax﹣1（e为自然对数的底数）．（Ⅰ）当a=1时，求过点（1，f（1））处的切线与坐标轴围成的三角形的面积；（Ⅱ）若f（x）≥x2在（0，1）上恒成立，求实数a的取值范围．【考点】利用导数研究曲线上某点切线方程；函数恒成立问题．【分析】（I）当a=1时，f（x）=e x+x﹣1，根据导数的几何意义可求得在点（1，f（1））处的切线的斜率，再由点斜式即可得切线方程，分别求出切线与x轴、y轴的交点A、B，利用直角三角形的面积公式即可求得；（II）将f（x）≥x2在（0，1 ）上恒成立利用参变量分离法转化为在（0，1 ）上恒成立，再利用导数研究不等式右边的函数的单调性，从而求出函数的最大值，即可求出a的取值范围．【解答】解：（I）当a=1时，f（x）=e x+x﹣1，f（1）=e，f'（x）=e x+1，f'（1）=e+1，函数f（x）在点（1，f（1））处的切线方程为y﹣e=（e+1）（x﹣1），即y=（e+1）x﹣1，设切线与x轴、y轴的交点分别为A、B，∴A，B（0，﹣1），∴，∴过点（1，f（1））处的切线与坐标轴围成的三角形的面积为．（II）由f（x）≥x2得，令h（x）=，，令k（x）=x+1﹣e x…k'（x）=1﹣e x，∵x∈（0，1），∴k'（x）＜0，∴k（x）在（0，1）上是减函数，∴k（x）＜k（0）=0．因为x﹣1＜0，x2＞0，所以，∴h（x）在（0，1）上是增函数．所以h（x）＜h（1）=2﹣e，所以a≥2﹣e。

南沙一中2015—2016学年第二学期期中考英语试题高二英语说明: 本试卷分为选择题和非选择题两部分，共8页，满分150分。

考试时间120分钟。

命题人：李小娜卢燕芹第一部分阅读理解（共两节，满分40分）第一节（共15小题，每小题2分，共30分）阅读下列短文，从每题所给的四个选项（A、B、C和D）中，选出最佳选项。

AChoose Your VirginiaRock House MuseumTake a journey through history with a visit to the exciting museum and historic sites of Wytheville. The Rock House Museum offers glimpses into daily life in the 19th century. The museum is part of the 50 structures featured in Wytheville's Historic Walking Tour. 540/223－3330.Natural Bridge of VirginiaNatural Bridge of Virginia, one of the Seven Natural Wonders of the World. Caverns of Natural Bridge, guided tours of underground wonders; Natural Bridge Inn & Conference Center, Indoor Heated Pool, largest Gift & Souvenir Shop in the East. Information 800/533－1410.Grand CavernsGrand Caverns is America's oldest show cave. Beautiful and massive formations. Union troops visited the caverns. Thomas Jefferson visited you should too! Open weekends in March, daily April～October, 9 a．m.～5 p．m. Hour tours leave every 30 minutes. 703/249－5705.The NewseumThe Newseum in Arlington, the world's only interactive museum of news. Visitors can be reporters or television newscasters, see today's news as it happens on a block－long video news wall, and be taken behind the scenes to see how news is made. The Newseum is open Wednesday through Sunday from 10 a．m.～5 p．m. 888/NEWSEUM. www. Newseum. Org.Kenmore Plantation & GardensKenmore Plantation & Gardens, visit over two hundred years of history from the Revolutionary War, Civil War and into the 21st－century. Home of Betty Washington, George Washington's only sister, and Patriot Col. Fielding Lewis. Explore this historic building and city block of restored gardens. Tea and ginger cookies served. 540/373－3381.Virginia BeachVirginia Beach offers 11,000 hotel/motel rooms, plus cottages and campgrounds. Enjoy miles of clean beaches and a variety of family attractions. Fine restaurants, various shopping areas, exciting nightlife, and special events are offered throughout the year. 800/822－3224.1．In what way is the Newseum different from Rock House Museum?A．It is larger.B．It is more exciting.C．Visitors can act in it.D．Visitors can see more in it.2．Which of the following places is NOT open in the winter months?A．Natural Bridge of VirginiaB．Grand CavernsC．Virginia BeachD．Kenmore Plantation & Gardens3．Which of the following is NOT true about Virginia Beach?A．Tourists can camp in the open air.B．Tourists can enjoy some special events there.C．Tourists can not go there in their own cars.D．Tourists can enjoy themselves on the clean beach.BRandy Kraus was paralyzed(瘫痪的). His left side was useless. He'd been a police officer before, and he could do strong and able. Now, he felt he could do nothing.His trouble started with Parkinson's disease, but it didn't end there. In July, 2002, the 60-year-old Kraus went into the hospital for an operation, on his brain to control the shaking. But he had a stroke(中风). He was paralyzed. The doctors said, “You may never walk again and you might not even be able to talk.”Kraus found that he couldn't lift a fork or take a drink by himself. Physical treatment was so painful and slow. What did he have to live for? So Kraus held the gun against his head. Feeling the cold metal on his skin, he began to consider the pain he would cause for his wife, daughters and grandchildren. He didn't pull the trigger(扳机)．Andrew Garud, his exercise physiologist(生理学家), told him，“You are where you are. The pace would be s low; the pain would be real. But as long as you are alive, you have the ability to get better.”After three months of working with Garud, Kraus wanted to see if he could stand. He could. Then he took three steps，sat down and cried like a baby.One step, as they say, led to another. Next he managed a short walk along the edge of a boxing ring(拳击台) in the health club. It was the hardest fight of Kraus's life. People at the gym cheered him on. Garud kept saying he could do more. Now, Kraus can brush his teeth, shave himself, and get around the house with a walker. Only the paralyzed can fully understand little triumphs.4．According to the fourth paragraph, what did Andrew Garud mean?A．Everyone in the world has the right to be alive.B．It' s necessary for people to do exercise to keep healthy.C．One should try to lead a better life.D．As long as a person is alive, he will have a chance to be better.5．What does the underlined word“triumphs”in the last paragraph mean?A．Difficulties. B．Successes.C．Disappointments. D．Reputations.6．What personality does Kraus probably have?A．Optimism. B．Strong-mindedness.C．Sympathy. D．Generosity.7．According to the passage, we can learn that ________.A．the stroke during the operation on his brain led to Kraus' paralysisB．Kraus' operation in 2002 was performed by Andrew GarudC．doing exercises can help cure Parkinson's diseaseD．Kraus will lead a normallife as a healthy person in the futureCMen are spending more and more time in the kitchen encouraged by celebrity (名人) chefs like Gordon Ramsay and Jamie Oliver，according to a report from Oxford University.The effect of the celebrity role models，who have given cooking a more manly picture，has combined with a more general drive towards sexual equality and men now spend more than twice the amount of time preparing meals than they did in 1961.According to the research by Prof.Jonatahn Gershuny, who runs the Centre for Time Research at Oxford，men now spend more than half an hour a day cooking，up from just 12 minutes a day in 1961.Prof.Gershuny said, “The man in the kitchen is part of a much wider social trend.There has been 40 years of sexual equality, but there is another 40 years probably to come.”Women，who a generation ago spent nearly two hours a day cooking，now spend just one hour and seven minutes—a great fall, but they still spend far more time in the kitchen than men.Some experts have named these men in aprons as “Gastrosexuals (men using cooking skills to impress friends)”，who have been inspired to pick up a kitchen knife by the success of Ramsay，Oliver as well as other male celebrity chefs such as Hugh Fearnley－Whittingstall, Marco Pierre White and Keith Floyd.“I was married in 1974.When my father came to visit me a few weeks later，I was wearing an apron when I opened the door.He laughed，” said Prof.Gershuny.“That would never happen now.”Two－thirds of adults say that they come together to share at least three times a week，even if it is not necessarily around a kitchen or dining room table.Prof.Gershuny pointed out that the family meal was now rarely eaten by all of its members around a table—with many “family meals” in fact taken on the sofa in the sitting room，and shared by family members.“The family meal has changed a lot，and few of us eat—as I did when I was a child—at least two meals a day together as a family.But it has survived in a different format.”8.What is one reason behind the trend that men spend more time cooking than before?A.The improvement of cooks'status.B.The influence of popular female chefs.C.The change of female's view on cooking.D.The development of sexual equality campaign.9.What does the author think about the time men and women spend on cooking?A.Men spend more time cooking than women nowadays.B.Women spend much less time on cooking than before.C.It will take 40 years before men spend more time at the stove than women.D.There is a sharp decline in the time men spend on cooking compared with 1961.10.How did Prof.Gershuny see the family meal according to the passage?A.It has become a thing of the past.B.It is very different from what it used to be.C.It shouldn't be advocated in modern times.D.It is beneficial to the stability of the family.11.Which is the best title for the passage?A.The Changes of Family MealsB.Equality between Men and WomenC.Cooking into a New Trend for MenD.Cooking—a Thing of the Past for WomenDI am trying to muster(鼓起) the courage to toss_away my mobile phone to enjoy a more peaceful and ring­free life.Can you imagine not having your mobile phone? In our hightech, in-a-hurry age, a cell-free life is a hard concept to swallow. Our mobile phones can now access the Internet, and many people feel the need to express their every thought on their blog pages. If I gave up my cellphone, people would think I was mad.I wish I had the strength to toss away my technology. I have an office phone，a home phone，e­mail and if people want to contact me, they can. If I'm out, people can leave a message. Do they really need to find me 24/7? However, I'm a bit like Frodo in the movie Lord of the Rings. The power of the ring is too strong and I can't let it go.Mobile phones have become necessary tools in our busy life. For most people, they hold all contacts and many of us don't write up address books any more. The latest phones carry our music, pictures, movies and everything else. We feel lost without this device and when we do misplace it, we feel cut off from our fellows.“Where have you been？”said a friend, who saw me a week after I lost my cell, “I tried calling you, but you disappeared. You disappeared off the face of the Earth. ”See, when you don't have a mobile phone，you don't exist.I'm not really going to toss my mobile phone away, in fact. We humans are such social animals and mobile phones serve us well. So in 2009, I've decided not to serve my mobile phone. Like all machines, I can always turn it off.12．What does the underlined phrase “toss away”mean?A. give away.B. get away.C. break away.D. throw away.13．The writer mentions Frodo to ________.A. show it is difficult to get rid of the mobile phoneB. show how much he likes FrodoC. suggest a cell-free life is what he wantsD. introduce a film character to us14．What do we know about mobile phones in the 4th paragraph?A. Mobile phones can do anything for us.B. Mobile phones have become very important in our life.C. We could not live without mobile phones.D. We would be cut off by our fellows without mobile phones.15．What can be inferred from the last paragraph?A. The writer is not really going to toss his mobile phone away.B. When you don't have a mobile phone，you don't exist.C. The writer decides not to serve his mobile phone.D. We humans can control ourselves and machines well.第二节（共5小题，每小题2分，满分10分）根据短文内容，从短文后的选项中选出能填入空白处的最佳选项。